This invention relates to transformational folding puzzle assemblies, and, more particularly, to a transformational ring of 24 isosceles tetrahedrons which can be used for educational, entertainment, or advertising purposes.
Rings of rotating tetrahedrons have been known for many years. The earliest known relevant patent, U.S. Pat. No. 1,997,022 to Stalker in 1933, presented the original use for such rings as an advertising medium or toy. While it mentions larger tetrahedron rings, the preferred embodiment (pictured in the patent) is a ring of six or eight isosceles tetrahedrons. The concept is described in Ball & Coxeter, Mathematical Recreations and Essays, along with an arrangement of the numbers from 1 to 32 by Heath on "a magic rotating ring" of eight regular (not isosceles) tetrahedra. Doris Schattschneider and Wallace Walker copyrighted various isosceles tetrahedron rings of 6 to 12 members which they covered with M. C. Escher tessellated patterns and termed them kaleidocycles. The entertainment value of Stalker's assembly and Walker/Schattschneider's rings involve the visual appearance and transformation of colors and images when the connected bodies are simultaneously rotated upon their individual axes (at opposite edges of the ring towards the center) to bring disparate surfaces into edge-adjacent, abutting relationship. For this particular effect it is important to have less tetrahedra (the minimum for a tetrahedron ring is six), generally six to eight.
Rings of tetrahedra that are meant to be "flipped and folded" to make solid geometrical shapes, rather than to make changing patterns, are also Unavailable. One such manifestation, made out of cloth hinges and plastic tetrahedrons features two colors and 12 irregular right tetrahedrons. Depicted on the descriptive packaging for this product are about 18 shapes that can be made by folding up the ring. The only graphic differentiation between the triangular paces of the tetrahedrons is that they come in two different colors. No means of holding the shapes together is given; in general the arrangements are held together simply by the inertial weight of the plastic tetrahedrons upon one another.
A major disadvantage of the prior art in relation to rotating tetrahedron rings concerns this separation between the two methods of designing tetrahedron rings. If the only effect desired from a rotating tetrahedron ring is the kaleidoscopic effect of different faces tumbling in towards the center of the ring as the ring is rotated about its closed loop axis, then the most important factor is that each of the four triangular faces of each tetrahedron in the ring be graphically different (either in color or design) and that the ring be of small size (6 to 12 tetrahedrons) so this effect can be easily seen. If the primary effect desired from a tetrahedron ring is that it contract to form various random solid shapes, the most important factor is that the tetrahedrons be "allspace-filling", so that there are no irregular gaps or voids between or among the surfaces of the contracted shape, and that the ring be of large size (12 or more tetrahedrons).
Prior art involving the arrangement of magic numbers on the surface of a rotating tetrahedron ring has several disadvantages. The only described version (Heath) has only one true connection with exterior shape, which is that there is a magic constant (the sum of all four triangles) for each tetrahedron contained on the ring. Other magic constants he describes involve tracing out patterns mentally as the viewer travels in a spiral fashion around the ring. Heath's version (published in Ball & Coxeter, Mathematical Recreations and Essays, p. 216) is depicted as consisting of equilateral triangles and makes a ring of eight regular tetrahedrons. It is a geometric fact that the regular tetrahedron is not an all-space filling tetrahedron. Thus this prior art "magic number" ring necessarily belongs to the category of tetrahedron rings which are meant to rotate towards the center and cannot be contracted into coherent solid shapes with no gaps between the tetrahedrons. Therefore, while Heath suggests a number of magic constants of greater magnitude than the sum of the triangles on every tetrahedron, none of them are related to a larger, contracted, all-space filling shape.
Accordingly, it would be desirable to have a rotating tetrahedron ring that has:
1) sufficient size to use the capacity of all-space filling tetrahedrons to be grouped to form a large plurality of geometric solid-shapes; and,
2) sufficient graphic intricacy involved in the color/design/arrangement of the triangular faces such that, at a minimum, each contracted shape has at least four visually distinct representations. In addition it would be desirable that in order to fully explore the potentials of the relationship between design and shape, that the shape be held together in such a way that it does not come apart when it is picked up. Accordingly an external or internal means should be provided for holding the tetrahedron ring together in various contracted shape configurations.